Why does the training time of SVMs dramatically decrease after applying dimensionality reduction to the features?
SVM complexity is $O(\max(n,d)\min(n,d)^2)$ according to Chapelle, Olivier. &quot;Training a support vector machine in the primal.&quot; Neural Computation 19.5 (2007): 1155-1178.
$n$ is the number of instances and $d$ is the number of dimensions. I'm assuming that you have more instances than dimensions giving a complexity of $O(nd^2)$. Hopefully this explains fully why reducing the number of dimensions will reduce the training time.